A functional equation for multiple zeta functions and generalized confluent hypergeometric functions

Abstract

In this paper, we introduce a new function, the multiple confluent hypergeometric functions, and establish a functional equation for the $r$-variable Euler--Zagier multiple zeta functions using it. In the case when $r=2$, this functional equation includes the well-known functional equation for the Euler--Zagier double zeta functions obtained by Matsumoto.